A shopkeeper sells a saree at 8% profit and sweater at 10% discount thereby getting a sum of Rs.1008. If she sold the saree at 8% discount , she would have got Rs.1028. Find the cost price of the saree and list price of the sweater.
Answers
and a sweater at 10 % discount, the shopkeeper gets Rs. 1008
⇒ 108x/100 + 90y/100 = 1008
⇒ 27x/25 + 9y/10 = 1008/1
Taking L.C.M. of the denominators and then solving it, we get.
54x + 45y = 50400 ............(1)
Situation 2 -
by selling a saree at 10 % profit and a sweater at 8 % discount, the shopkeeper gets Rs. 1028.
⇒ 110x/100 + 92y/100 = 1028
⇒ 11x/10 + 23y/25 = 1028/1
Taking L.C.M. of the denominators and then solving it, we get.
⇒ 55x + 46y = 51400 ...........(2)
Now, multiplying the equation (1) by 55 and (2) by 54, we get.
(54x + 45y = 50400)*55
= 2970x + 2475y = 2772000 ............(3)
(55x + 46y = 51400)*54
= 2970x + 2484y = 2775600 .............(4)
Now, subtracting (3) from (4), we get.
2970x + 2484y = 2775600
2970x + 2475y = 2772000
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9y = 3600
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⇒ 9y = 3600
y = 3600/9
y = 400
Putting the value of y = 400 in (1), we get.
54x + 45y = 50400
54x + (45*400) = 50400
54x + 18000 = 50400
54x = 50400 - 18000
54x = 32400
x = 32400/54
x = 600
So, the cost price of a saree is Rs. 600 and the list price of a sweater is Rs. 400